The Physics of Flow

If there is one concept in resuscitative medicine that has long perplexed many a “self-proclaimed resuscitaionist”, it is the battle between pressure gradient and resistance in cardiac arrest and how these should guide your resuscitation. The physics buffs out there may recognize the equation V=IR as Ohm’s law, written another way,I=V/R we can begin to appreciate its true beauty in the context of physiology. Ohm’s law is synonymous with the flow equation we use in medicine; Q=ΔP/R where Q= flow, ΔP= change in pressure or (MAP-RAP), and R=resistance or SVR. The flow equation my friends, IS the essence of life, it is what makes the blood go round and round. So let’s get into why you should develop a true appreciation for this little mathematical marvel and how you can use it to optimize your resuscitation.

The Nerdy Part
Dissecting the flow equation, if we increase ΔP, we will increase flow (Q), makes sense right? This is the current reasoning behind giving epinephrine in cardiac arrest, squeeze the tank and pressure goes up. The problem is, resistance (R) pays the greatest price to effect an increase in pressure which can ultimately lead to a reduction in flow (not good!). Epinephrine is a vasopressor with potent alpha and beta effects, the alpha effects of which are responsible for “squeezing the tank” which helps to raise the total pressure in the vessels and generate the often cited “golden 15mm/hg” necessary to perfuse the coronary arteries if ROSC is to be achieved. Unfortunately, this pressure change happens at the expense of exponentially increasing the resistance! A significant component of resistance in the flow equation is vessel diameter, resistance is inversely proportional to vessel radius diameter. In fact, in the famous Poiseuille equation, resistance or R= 8Ln/πr^4. Which means that in our Flow equation Q=ΔP/R, the effect that vessel radius has on resistance is immensely huge, it’s raised to the fourth power! Resistance is also inversely proportional to flow, i.e. an increase in R causes a decrease in Q or flow. In simple terms, a reduction in vessel diameter of 50% causes a 16-fold increase in resistance! What we end up with, is something not quite as simple as “give them Epi, increase their coronary perfusion pressure, and get ROSC”. This is the reason I want to try and talk you off the ledge of using empirical epinephrine in every cardiac arrest that comes through the door, or at least to stop using it the way we’ve always been taught to in ACLS.

(When I first wrote this, I wanted very badly to convince you all to throw your Epi in the trash and forget it ever existed, but in the words of the resuscitationist extraordinaire Scott Weingart, I will not be a nihilist. After all, that’s why I’m here in the first place talking about resuscitative medicine, because we should always be questioning whether what we are doing is working or not. There is some interesting data floating around on appropriate usage and dosing of epinephrine in cardiac arrest and I plan to talk more about these in a future piece, so stay tuned!)

Now, back to the discussion at hand. Our main focus should be on ACTUAL flow, it’s not enough to squeeze the tank and increase pressure if the resistance required to do so actually impedes flow. The indicator of flow we should be most concerned with in a cardiac arrest is not a pressure measurement, it is ETCO2. It is this measure which actually reflects how effectively we are moving oxygen and CO2 back and forth in the periphery and which tells us about the quality of our resuscitation. If we are achieving a good ETCO2 then the pressure at which that is happening is arbitrary because “air is going in and out and blood is going round and round”

What’s Next?
Much of what we are seeing on the leading edge of resuscitative science is directed at improving flow by loosening the tank with drugs like Nipride, or by supplementing the flow externally as in ECMO and ECPR. The body’s natural response to a lack of flow or ischemia, is a process called reactive hyperemia, whereby the ischemic tissue actually causes dilation of vessels to try and increase flow to the area in order to resolve the oxygen debt. The question we should be asking ourselves in a resuscitation is, how can we mimic reactive hyperemia in a cardiac arrest patient by generating a level of flow capable of producing gas exchange? After all, the whole point of this is to provide gas exchange at the cellular level. In a perfect world we would be able to supplement flow and augment resistance to support a pressure that is capable of good perfusion. (Like we get with ECMO and ECPR) In my opinion, this is achievable with some common CPR adjuncts and good implementation of basic resuscitation, while monitoring ETCO2 as a reflection of flow and quality of resuscitation, and then selectively implementing vasoactive drugs at appropriate times and doses which don’t work against you or compound the post resuscitation syndrome experienced by many resuscitated patients.

Final Thoughts
We would do well to remember that using Epinephrine or many of the other vaso-“pressive” agents to support pressure is not without consequence, and that for flow to increase, resistance must decrease. Cardiac arrest results in a lack of blood flow to ALL of the tissues, not just the heart, we would do well to target our resuscitation efforts to the cellular level, and if we do that, surrogates like pressure measurements and down times will take care of themselves.

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